He said: "There is no clause in the contract. My last game is Sunday. I have had an incredible time and hopefully I will end with the best ending possible.
"I have had no contact with the president about anything else and I first realised I would be leaving Real in January when I was told my contract wouldn't be renewed.
"I knew I had to decide my future and leaving a club like Real Madrid is very difficult.
"But the future is very bright and something I'm really looking forward to now. But I'll miss Real Madrid and Spain a huge amount.
"I made a decision, I had to. I needed to make a decision and my option was the United States. I'm very happy about that decision, it's a very exciting prospect."
"The Real Madrid fans have been incredible, not just to me but to my family. That is something I will never forget in my whole life," he added.
"I have to say thank you for that. I could without a doubt have stayed for two or three more years, I could have stayed for the rest of my career but things change.
"I have a lot of respect for the president and Fabio Capello, he is one of the best managers in football."
Beckham was unable to train alongside his Madrid team-mates for the first two sessions of the week due to the ankle injury he picked up on England duty.
But the signs were more positive today as he jogged around the pitch at the club's Valdebebas training ground alongside fitness coach Jose Luis San Martin ahead of Sunday's crunch clash with Mallorca.
Beckham is yet to win any silverware with Madrid but believes victory - and the title it will guarantee - would be the perfect way to bring down the curtain on his career in Spain.
He added: "I haven't won anything in four years (at Madrid) and hopefully I can change that on Sunday.
"My best memory so far was signing for Real Madrid, I'm hoping that will change on Sunday, when my memories here will be taken to another level by winning something.
"I hope to reward the fans with a trophy."
